Yes if you get the right software for it. I don't do it that way. I prefer to use makemkv, put the file on an external disk, attach it to my tv and watch it that way.
Early 2009 is 2.26Ghz I presume, and yes that plays BR fine with MacBluRay Player. MakeMKV is also an option, I use that too and play the MKV's with XBMC on the Mini.